Mohammed probably couldn’t have been syphilitic. Syphilis likely came from America and wasn’t known in the Old World until after Columbus.
Debate about the origins of syphilis has continued for nearly 500 years, ever since early sixteenth-century Europeans blamed each other, referring to it variously as the Venetian, Naples, or French disease. One hypothesis assumes a New World origin, and holds that sailors who accompanied Columbus and other explorers brought the disease back to Europe. Another explanation is that syphilis was always present in the Old World but was not identified as a separate disease from leprosy before about A.D. 1500. A third possibility is that syphilis developed in both hemispheres from the related diseases bejel and yaws. New studies by paleopathologists Bruce and Christine Rothschild favor a New World origin.
I'll stick with my descriptor of mutthomed, it takes me to a happy place.
That theory is coming under serious doubt
Here's just one article that possible refutes it...
http://www.bbc.com/news/world-europe-11952322